What are the definitions of bounded and unbounded functions and how to judge whether a function is bounded or unbounded? Let me start with a few questions 1. Is f (x) ∈ (a, b), f (x) bounded? G (x) ∈ [a, b], the upper bound of G (x) is B, the lower bound is a, which should be right 2. Functions with limits are not necessarily bounded? For example 3. Does f (x) unbounded represent f (x) →∞ when x ∈ (a, b), or other?

Definition: suppose f is a function of D - > R, if there is a real number m such that f (x) = m holds for all x ∈ D, then f has a lower bound, and M is a lower bound of F

What functions are not integrable except those defined in open intervals and unbounded functions?

Dirichlet function is defined as follows:
When d (x) = 1 and X is a rational number
When d (x) = 0 and X is irrational

The following functions are unbounded in the definition
A Y=sin（x+2）
B Y=5-cosx
C Y=cotx
D Y=3+COSx^2

When x tends to zero, y tends to infinity

Classic mathematical problems
One day during the winter vacation, each of them gave a dime to buy a table tennis ball together. They spent 25 cents to get back five cents. Each of them got one cent that time, and two cents to buy three pieces of sugar. Later, the three calculated and said they were one cent short. They said, "originally, we each gave a dime, but later we got one point back from the money we got back, In addition to nine cents, 3927 cents and two cents for buying sugar, there is only twenty-nine cents for each person. Where is the other one? "Please think about it carefully
To explain the reason, to points please avoid

In fact, it's the people who have problems guiding us in the wrong direction. The 25 cents for buying table tennis and the 2 cents for buying sugar are the 27 cents spent. The remaining 3 cents are in everyone's pocket, a total of 3 cents

Use a piece of iron wire to form a square with a circumference of 31.4 decimeters. Use this iron wire to form a circle. How many square decimeters is the area of this circle?

Radius of circle = circumference △ 2 △ π = 31.4 △ 2 △ 3.14 = 5 (decimeter)
The area of the circle = π × radius & # 178; = 3.14 × 5 & # 178; = 78.5 (square decimeter)
A: the area of the circle is 78.5 square decimeters

N = 10 * (2000 ^ 2001 + 2001 ^ 2002) / (2000 ^ 2000 + 2001 ^ 2001), find the integer part of n

Let 2000 ^ 2000 = a, 2001 ^ 2001 = B
n/10=(2000a+2000b+b)/(a+b)
=2000+b/(a+b)
Because B / (a + b) > b / (2001 ^ 2000 + b) = 0.9995
So n / 10 = 2000.9

In recent years, Shanghai has invested a lot of money to improve the urban traffic, and the traffic condition has been improved to a certain extent, but people's Square is still one of the most congested areas in the center of the city. In order to ensure traffic safety, it is stipulated that in this section, the vehicle distance D is a positive proportional function of the product of the square of the speed V (km / h) and the body length s (m), and the minimum vehicle distance should not be less than half of the body length, It is assumed that the speed is 50 km / h and the distance is just the body length
(1) try to write the analytic formula of D with respect to V (where s is a constant);
(2) what kind of speed should be specified to maximize the traffic flow Q = (1000V / (D + s))?
Do the units here need to be unified? Why do our teachers go on without unified units?
Just answer the above questions

There is no need to unify, d = k · V & sup2; · s, the dimension on the left is meter, and the dimension on the right is km & sup2; × M / H & sup2; without considering K, so it can be considered that K implies the dimension of hour & sup2; / km & sup2;. Therefore, we can directly use the unit specified in the mathematical model given in the question to calculate

A square, its side length increases 8 cm, the area increases 224 square cm, find the side length of the square

Suppose: the side length is xcm, then
(X+8)(X+8)-X*X=224
The solution is x = 10
So its side length is 10 cm

A round light spot in the shade of a tree is the image of the sun on the ground through the small holes between the leaves. Now the diameter of the light spot is 0.7cm
The distance between the sun and the earth is 1.5x10 ^ 11m, from which the diameter of the sun can be estimated to be____________ m.
Junior two physics, which big brother help to do next
The distance between the spot and the hole is 7.5m

Similar to a triangle, this one needs to know the height h of the leaves from the ground, and then the diameter of the sun is
D=0.7/H×1.5×10^11
Generally speaking, leaves are about 200 cm from the ground. You can bring them in and get the answer

Physical meaning of stress partial tensor and stress sphere tensor

To explain this problem, we should begin with the stress state
The stress set of all sections at a certain point is called the stress state of this point. The stress state is not scalar or vector, but tensor, which is different from vector and has multiple directivity. It is generally expressed by matrix s
The matrix s can be divided into two parts: S = s 1 + S 2, where s 1 is called stress sphere tensor and S 2 is called stress partial tensor
S1 is the average and uniform tension or compression decomposed from the total stress state, which only causes the change of elastic volume, but does not change the shape
S2 indicates that the shape of the object unit changes but the volume does not change
In plasticity, only S2 is concerned
In summary, the stress state is artificially divided into two parts, one represents the volume change, the other represents the shape change. According to the experiment and practical application, the correctness of the derivation is verified, so the stress partial tensor can represent the deformation of the object
The specific derivation needs to refer to the relevant works. This problem is elaborated in the book tensor analysis edited by Huang Kezhi